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  <div class="section" id="numpy-random-randomstate-standard-gamma">
<h1>numpy.random.RandomState.standard_gamma<a class="headerlink" href="#numpy-random-randomstate-standard-gamma" title="Permalink to this headline">¶</a></h1>
<p>method</p>
<dl class="method">
<dt id="numpy.random.RandomState.standard_gamma">
<code class="sig-prename descclassname">RandomState.</code><code class="sig-name descname">standard_gamma</code><span class="sig-paren">(</span><em class="sig-param">shape</em>, <em class="sig-param">size=None</em><span class="sig-paren">)</span><a class="headerlink" href="#numpy.random.RandomState.standard_gamma" title="Permalink to this definition">¶</a></dt>
<dd><p>Draw samples from a standard Gamma distribution.</p>
<p>Samples are drawn from a Gamma distribution with specified parameters,
shape (sometimes designated “k”) and scale=1.</p>
<div class="admonition note">
<p class="admonition-title">Note</p>
<p>New code should use the <code class="docutils literal notranslate"><span class="pre">standard_gamma</span></code> method of a <code class="docutils literal notranslate"><span class="pre">default_rng()</span></code>
instance instead; see <em class="xref py py-obj">random-quick-start</em>.</p>
</div>
<dl class="field-list simple">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><dl class="simple">
<dt><strong>shape</strong><span class="classifier">float or array_like of floats</span></dt><dd><p>Parameter, must be non-negative.</p>
</dd>
<dt><strong>size</strong><span class="classifier">int or tuple of ints, optional</span></dt><dd><p>Output shape.  If the given shape is, e.g., <code class="docutils literal notranslate"><span class="pre">(m,</span> <span class="pre">n,</span> <span class="pre">k)</span></code>, then
<code class="docutils literal notranslate"><span class="pre">m</span> <span class="pre">*</span> <span class="pre">n</span> <span class="pre">*</span> <span class="pre">k</span></code> samples are drawn.  If size is <code class="docutils literal notranslate"><span class="pre">None</span></code> (default),
a single value is returned if <code class="docutils literal notranslate"><span class="pre">shape</span></code> is a scalar.  Otherwise,
<code class="docutils literal notranslate"><span class="pre">np.array(shape).size</span></code> samples are drawn.</p>
</dd>
</dl>
</dd>
<dt class="field-even">Returns</dt>
<dd class="field-even"><dl class="simple">
<dt><strong>out</strong><span class="classifier">ndarray or scalar</span></dt><dd><p>Drawn samples from the parameterized standard gamma distribution.</p>
</dd>
</dl>
</dd>
</dl>
<div class="admonition seealso">
<p class="admonition-title">See also</p>
<dl class="simple">
<dt><a class="reference external" href="https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.gamma.html#scipy.stats.gamma" title="(in SciPy v1.4.1)"><code class="xref py py-obj docutils literal notranslate"><span class="pre">scipy.stats.gamma</span></code></a></dt><dd><p>probability density function, distribution or cumulative density function, etc.</p>
</dd>
<dt><a class="reference internal" href="numpy.random.Generator.standard_gamma.html#numpy.random.Generator.standard_gamma" title="numpy.random.Generator.standard_gamma"><code class="xref py py-obj docutils literal notranslate"><span class="pre">Generator.standard_gamma</span></code></a></dt><dd><p>which should be used for new code.</p>
</dd>
</dl>
</div>
<p class="rubric">Notes</p>
<p>The probability density for the Gamma distribution is</p>
<div class="math">
<p><img src="../../../_images/math/9ae916d1bcb675510f8f5d6cac596ec4ff6d8af1.svg" alt="p(x) = x^{k-1}\frac{e^{-x/\theta}}{\theta^k\Gamma(k)},"/></p>
</div><p>where <img class="math" src="../../../_images/math/9630132210b904754c9ab272b61cb527d12263ca.svg" alt="k"/> is the shape and <img class="math" src="../../../_images/math/8a87f04e7d7cca18343c084cceca5237fae62491.svg" alt="\theta"/> the scale,
and <img class="math" src="../../../_images/math/e7003fd3463f843ee1e53385878369f078d362ad.svg" alt="\Gamma"/> is the Gamma function.</p>
<p>The Gamma distribution is often used to model the times to failure of
electronic components, and arises naturally in processes for which the
waiting times between Poisson distributed events are relevant.</p>
<p class="rubric">References</p>
<dl class="citation">
<dt class="label" id="r190e68b4b0fb-1"><span class="brackets">1</span></dt>
<dd><p>Weisstein, Eric W. “Gamma Distribution.” From MathWorld–A
Wolfram Web Resource.
<a class="reference external" href="http://mathworld.wolfram.com/GammaDistribution.html">http://mathworld.wolfram.com/GammaDistribution.html</a></p>
</dd>
<dt class="label" id="r190e68b4b0fb-2"><span class="brackets">2</span></dt>
<dd><p>Wikipedia, “Gamma distribution”,
<a class="reference external" href="https://en.wikipedia.org/wiki/Gamma_distribution">https://en.wikipedia.org/wiki/Gamma_distribution</a></p>
</dd>
</dl>
<p class="rubric">Examples</p>
<p>Draw samples from the distribution:</p>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="n">shape</span><span class="p">,</span> <span class="n">scale</span> <span class="o">=</span> <span class="mf">2.</span><span class="p">,</span> <span class="mf">1.</span> <span class="c1"># mean and width</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">s</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">standard_gamma</span><span class="p">(</span><span class="n">shape</span><span class="p">,</span> <span class="mi">1000000</span><span class="p">)</span>
</pre></div>
</div>
<p>Display the histogram of the samples, along with
the probability density function:</p>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="kn">import</span> <span class="nn">matplotlib.pyplot</span> <span class="k">as</span> <span class="nn">plt</span>
<span class="gp">&gt;&gt;&gt; </span><span class="kn">import</span> <span class="nn">scipy.special</span> <span class="k">as</span> <span class="nn">sps</span>  
<span class="gp">&gt;&gt;&gt; </span><span class="n">count</span><span class="p">,</span> <span class="n">bins</span><span class="p">,</span> <span class="n">ignored</span> <span class="o">=</span> <span class="n">plt</span><span class="o">.</span><span class="n">hist</span><span class="p">(</span><span class="n">s</span><span class="p">,</span> <span class="mi">50</span><span class="p">,</span> <span class="n">density</span><span class="o">=</span><span class="kc">True</span><span class="p">)</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">y</span> <span class="o">=</span> <span class="n">bins</span><span class="o">**</span><span class="p">(</span><span class="n">shape</span><span class="o">-</span><span class="mi">1</span><span class="p">)</span> <span class="o">*</span> <span class="p">((</span><span class="n">np</span><span class="o">.</span><span class="n">exp</span><span class="p">(</span><span class="o">-</span><span class="n">bins</span><span class="o">/</span><span class="n">scale</span><span class="p">))</span><span class="o">/</span>  
<span class="gp">... </span>                      <span class="p">(</span><span class="n">sps</span><span class="o">.</span><span class="n">gamma</span><span class="p">(</span><span class="n">shape</span><span class="p">)</span> <span class="o">*</span> <span class="n">scale</span><span class="o">**</span><span class="n">shape</span><span class="p">))</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">bins</span><span class="p">,</span> <span class="n">y</span><span class="p">,</span> <span class="n">linewidth</span><span class="o">=</span><span class="mi">2</span><span class="p">,</span> <span class="n">color</span><span class="o">=</span><span class="s1">&#39;r&#39;</span><span class="p">)</span>  
<span class="gp">&gt;&gt;&gt; </span><span class="n">plt</span><span class="o">.</span><span class="n">show</span><span class="p">()</span>
</pre></div>
</div>
<div class="figure align-default">
<img alt="../../../_images/numpy-random-RandomState-standard_gamma-1.png" src="../../../_images/numpy-random-RandomState-standard_gamma-1.png" />
</div>
</dd></dl>

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